3 A should be enough for the Galileo board and quite a bit of extra stuff... Bluetooth and LCD shouldn't be a problem.
3 A at 5 V is 15W, which is quite a lot for a small board. If a cell phone used that much, it would die in like 20 min. ;-)
You could start out by measuring how much the setup uses with a multimeter - my guess is closer to 1 A, maybe 1.5 A, but it's good that the power supply is a bit bigger than just good enough.
It's gonna be interesting to see if the solar panels can keep a charge on the batteries, but that depends on a lot of factors like size and quality of the panel and of course not least location on planet earth.
/Thomas